LA-731 O

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Tritium Production in a Sphere of 6LiD

Irradiated by 14-MeV Neutrons

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UNITCD STATESDEPARTMENT OF ENCR~VCONTRACT W-740 S-SN0. SC

LA-731O

UC-34CIssued: October 1978

Tritium Production in a Sphere of 6LiD

Irradiated by 14-MeV Neutrons

A. HemmendingerC. E. RaganE. R. ShunkA. N. Ellis

J. M. AnayaJon M. Wallace

t-

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CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...1

PART IMEASUREMENT OF TRITIUMPRODUCTION INASPHEREOF

‘LiDIRRADL4TED BY14-MeVNEUTRONS

ABSTRACT . . . . . . . . . . . .

I. INTRODUCTION . . .

II. THE6LiD ASSEMBLY

III. STANDARDIZATIONA.B.c.D.E.

General Procedure .Backgrounds . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Thermal Activations ofLiH.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...7 -Gamma-Ray Countingof’’’Au. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...8Calculation ofExpectedTritium Activity . . . . . . . . . . . . . . . . . . . . . . . . ...8

Iv. TRITIUM-PRODUCTION RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...11

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...12

APPENDIXA.

APPENDIXB.

APPENDIXC.

REFERENCES

TRITIUM DECAY RATES ENSAMPLES OF UNIRRADIATED’LiD ..13

CALCULATION OFVOLUME-AVERAGED NEUTRONFLUENCE . ..14

NEUTRON AND GAMMA-RAY ABSORPTION IN GOLD WIRE . . ...14

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

PART IICALCULATIONS OF TRITIUM PRODUCTION ANDRADIOCHEMICAL ACTIVATION IN A SPHERE OF

%iD IRRADIATED BY 14-MeV NEUTRONS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...17

L

II.

III.

Iv.

v.

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...17

CALCULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...17A. CalculationB. CalculationC. CalculationD. Calculation

I—ID, n-Group, S4Pl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...1811—lD,21-Group, S8Pl . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...18lll-lD, Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..18IV—3D, Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..’20

TRITIUM PRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...21A. Tritium Production From7Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...21B. Tritium Production From6Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...22

RADIOCHEMICAL ACTIVATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...24A. The (n,2n) Activations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...24B. The (n,f) Activations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...28C. The (n,7) Activations . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . ...29D. The l%(n,n’)19smIrActivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...31

CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...31

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ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...32

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...32

vi

TRITIUM PRODUCTION IN A SPHERE OF %iD

IRRADIATED BY 14-MeV NEUTRONS.

by..

.A. Hemmendinger, C. E. Ragan, E. R. Shunk,A. N. Ellis, J. M. Anaya, and Jon M. Wallace

.. \

ABSTRACT

The specific production of tritium in sampleo of ‘LW and ‘I&I embeddedin a 600-mm-diam sphere of OLiD irradiated by a central source cf 14-MeVneutrons has been detmmined by measuring the activity of the hydrogenevolved from the samples of each isotope at each of five different radii in theOLiD assembly. The entire process of decomposing the LiH, transferring the

evolved gas into counters, and determining the decay rate was standardizedby processing IJH samples irradiated by thermal neutrons for which the%i(n,a) cross’ section is well known.

The specific production of tritium in ‘LiH and TAH (embedded samples)and the activation of radiochemical detector foils of %c, ‘Y, ‘Zr, 1%,1’lIr.~7,‘WIr.8~, lWAU, ‘U, and ‘W placed at various positions in the ‘LiDsphere have been calculated and compared with the experimental data. One-and three-dimensional Monte Carlo and S. neutron-transport calculationswere performed. The most reliable (three-dimensional Monte Carlo)

calculation is in reasonable agreement with both the tritium-production andthe radiochemical-activation data. The existing discrepancies betweencalculation and experiment appear largely attributable to uncertainties insome tritium-production and radiochemical-activation cross sections.

.-

*

PART I

MEASUREMENT OF TRITIUM PRODUCTION IN A SPHERE OF%iD HUtADIATED BY 14-MeV NEUTRONS

by.

A, Henunendinger, C. E. ~an, E. R. Shunk,A, N. Ellis, and J. M. AUWa

ABSTRACT

The opecific production of tritium in ● 606-mmdiam sphere of %iD ir-radiated by a central source of 14-MeV neutrons has been determined byrnaaouring the activity of the tritium in samples of ‘LiH and ‘LiH containedin sealed quartz ●mpulea embedded in the sphere. Results are reported forseveral umplea of each isotope at each of five different radii in the as-wmbly. The entire process of decomposing the LiH sampleu, transferringthe evolved Cas into counters, and determining the decay rate was stan-dardiaad by procemins LiH samples irradiated by thermal neutrons forwhich the ‘Li(n,a) cross section is well known.

——.—————————————————

I. INTRODUCTION

The determination of the amount of tritiumproduced in a blanket of lithium surrounding aneutron source has long been of interest in connec-tion with nuclear weapons and controlled ther-monuclear reactora. If a sustained thermonuclearreaction requires tritium as a fuel, the only plausibleway to keep such a system operating would be tocreate tritium as a by-product of 14-MeV neutronsproduced in the reactor. In 1956 Marvin Wyman*reported the tritium production in samples of ‘L1metal embedded in a 600-mm-diam sphere of LiDsurrounding a source of 14-MeV neutrons. Hisresults confirmed that tritium is indeed produced insubstantial quantities by the reaction ‘Li(n,n’a).

Several measurement of tritium production inblanketa containing natural lithium are shown to bein fair agreement with calculations.s-’ Muir andWyman’ and Qaim, Wtilfle, and St&klin” have dis-cussed the need for integral data on tritium produc-tion, and they have analyzed earlier experiments.

We report here an experiment, similar toWyman’s, in which we irradiated an assembly of‘LiD containing test samples of ‘LiH and 7LiH.Teledyne Isotopes, Inc., Westwood, NJ 07675,analyzed these samples by evolving hydrogen fromthem and counting the tritium decay by a methodresembling, but developed independently of, thatdescribed by Qaim.7 Our experiment, which wasdesigned to investigate the transport of neutrons inOLiD and tc determine the tritium production,provides benchmark measurement for comparisonwith calculations. Results for tritium production in“ .i in such an assembly have not previously beenrepmted.

IL THE ‘LiD ASSEMBLY

Nesting hemispherical shells of ‘LiD were con-structed to fit around the target assembly of aCockcroft-Walton (C-W) accelerator. The inside andoutside diameters of the assembly were 44.4 and 600

.

.

.

2

mm. Details of dimensions, masses, and isotopiccomposition are given in Table I. Small cavities atthe shell interfaces held samples of 6LiH and ‘LiH;these samples were in sealed quartz ampules (Fig. 1)in two sizes: 10-mm o.d. for the two inner-shell inter-faces and 18-mm o.d. for the outer shells. The am-pules were filled, weighed, and sealed in an at-mosphere of helium.* All ampules were taped inplace in the assembly, as shown in Fig. 2. At leasttwo empty ampules (treated in the same manner asthe filled ampules) were positioned at each radiusfor background measurement.

The neutron-source flux distribution wasmeasured over 47rsr using both liquid-scintillator

*M ‘LID parta and LIH samples were prepared by Union CarbideCorporation, Oak Ridge, TN 37830.

TABLE I

SPECIFICATIONS FOR ‘LID

HEMISPHERICAL SHELLS

Diameter (mm)Mass %i

Inside Outside (kg)— . _

44.4 100.0 0.1783

0.151

102.0 152.3 0.449

0.490

154.3 252.0 2.465

2.330

254.0 400.0 9.133

9.430

402.0 600.0 30.000

29.200

Total mass = 83.826

(at.%)

95.59

95.59

95.59

95.68

95.68

(Wt%)

94.89

94.89

94.89

95.00

95.00

uH8 OR16mm

1-10 OR18mm 4

Fig. 1.Quartz ampule, with dimensions for two sizes,which held the lithium hydride samples for ir-radiation.

Fig, 2.Lithium hydride samples taped in place incavities in the 8LiD hemishell.

AZMJTH 8 (dq)50 I I I I 44s A

8—G; :b-f00

4s a e A44L

50?-4-7

1- •i~0

POLAR ANGLE + (dog)

Fig. 3.Map of the neutron flux over the sphere aroundthe C-W machine target. The measurementsmade wing a NE-213 (Nuclear Enterprises,Inc.) scintilZator biased at 12 MeVare shown ascircles, and those obtained using a cadmium-shielded ‘86(J fission detector are shown astriangles.

and fission detectors. This distribution is displayedin Fig, 3 as a function of the azimuthal angle 0 (0°being the direction of the deuteron beam) and thepolar angle O, the angular displacement about theaxis defined by the deuteron beam (0° being in thehorizontal plane to the right side looking into thebeam). The observed flux distribution is not quiteisotropic because of a superposition of two effects:(a) neutron emission from the recoiling compoundnucleus varies relative to the 90° flux by +5% in theforward direction to –57. in the backward directionand (b) the flux is attenuated by about 10”Ain direc-tions in which neutrons traversethe target backing.

The copper target wafer, which had a surface layerof tritium embedded in titanium, was oriented in avertical plane at an angle 45° from the direction ofthe horizontal deuteron beam. The ‘LiH samples inthe assembly were located in the vertical – 110°plane (B-B), the ‘LiH in the vertical –65° plane (A-A), as shown in Fig. 4. The location of a sample ineither plane is specified by its radius r and by a polarangle w measured from the parting plane lookinginto the beam. Care was taken in positioning thesamples to avoid locations at which there might be aneutron flux perturbation; thus no two ampules wereplaced along the same radius, near the parting planeof the sphere, or in the plane of the C-W target wherethere are flux perturbations as large as +8%. Theseprecautions were taken even though variations inthe flux were probably smoothed out at distancesgreater than one mean free path in the ‘LiD—108“mm for 14-MeV neutrons.

Figure 5 shows the lower half of the assembly inplace around the target, and Fig. 6 shows the par-tially completed ‘LiD assembly. The assembly wassupported in a 520-mm-diam hole in a 6.4-mm-thickcircular aluminum plate. The plate was suspendedfrom an assembly frame (Fig. 7) constructed tomount massive objects around the C-W machinetarget.

111. STANDARDIZATION

A. General Procedure

To evolve hydrogen from lithium hydride,Teledyne crushed each quartz ampule in a stainlesssteel tube that they heated until there was no furtherevolution of gas. The volume of the evolvedhydrogen was measured, and hydrogen carrier wasadded to the small samples only. The hydrogen gaswas converted to water, and the water was dilutedand divided into several parts in measured ratios. Toassay one of these subdivided samples, they con-verted it back to hydrogen and transferred the gasinto a shielded proportional counter.

In addition, a portion of the tritiated water fromeach sample was mixed with a liquid scintillator,and the sample count rate was determined.Teledyne calibrated the counting system routinelyby counting part of a standard sample, NBS 4925,

,

t

4

. .

. .

Fig. 4.

Schematic showing positions of lithium hydride samples in the “LiD assembly.cles for some samples indicated that the stem of the ampule is toward theangles above the parting plane are negatiue.

which they had used for about 10 years; thisprovided Teledyne’s primary standard. They usedtwo additional calibration methods:

(1) counting a fraction of NBS 4926 standardsample, which had been calibrated by theNational Bureau of Standards on 1July 1976;

(2) comparing Teledyne’s count on a fraction ofour sample 327 with NBS’s count on anotherfraction of the same sample.

The small cir-observer. The

A comparison of calibrations 1 and 2 (Table II)shows that the Teledyne and NBS determinations oftritium activity agree within 1.5Y0,which is withinTeledyne’s standard deviation. NBS estimates theirsystematic error at 20A;this is the same systematicerror inherent in the Teledyne measurement,because both groups used fractions of the sametritium standard source.

5\

Fig. 5.Bottom half shells of the 8LiD assemblymounted around the target of the C-Wmachine. The tube at the lower left is for targetinsertion and cooling; at upper left is the beamentry tube, and at upper right is the alphu-particle counter tube for monitoring theneutron flux.

Fig. 6.Shells of 8LiD mounted around the tritiumtarget of the C-W machine. The bottom half ofthe assembly is complete; the outer top threehemishells are missing.

Because there may be other systematic errors,which we believe are associated with gas handling byTeledyne (see Sec. I.11.E),tritium production resultsin lithium hydride irradiated by thermal neutronswere used to calibrate the whole process of gashandling and counting. These lithium hydride sam-ples, each containing a gold fluence monitor, were ir-radiated in the thermal column of the Los AlamosScientific Laboratory (LASL) Omega West Reactor.The ratio of the thermal capture cross section of ‘Lito that of I’”Au is well enough known””’ that tritiumcounting by Teledyne of these reactor-irradiatedsamples provided a calibration of Teledyne’smeasurements relative to the absolute counting ofthe gold by LASL.

. .

..

Fig. 7.Completed 6LiD assembly surrounding thetarget of the C-W machine. The aluminum cir-cular mounting plate is suspended from apneumatic assembly machine by three rods.Three sample ampules can be seen on the out-side surface.

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TABLE II

COMPARISON OF TRITIUM DETERMINATIONS IN WATER

Sample

NBS H-3

LASL-327

B. Backgrounds

BY TELEDYNE AND NBS

Teledyne Measurement NBS MeasurementRef. Date [108dis”s-’”(g H,O)-’] [l& dis”s-’”(g H,O)-l]

8/16/76 2.2422.292

av=~10/11/76 1.960

A surprise came in our investigation of samples ofLiD, the material that we originally intended to usein the ampules, for they had tritium backgroundshigh compared with the activation expected in theC-W irradiations. For completeness, we report thesebackground levels in Appendix A. Inasmuch as thedeuterium abundance in our LiD was typically 99.9at.%, it is reasonable to suppose that an increase ofthe deuterium content by a factor of 7000 above thenatural level will necessarily increase the tritiumfraction of hydrogen even more; the natural abun-dance of tritium augmented by enrichment appearssufficient to account for the observed backgrounds.In our samples of ‘LiH, the tritium background wasbelow Teledyne’s detection limit; the samples of7LiH contained appreciably more tritium, but nevermore than a few per cent of the activity induced byirradiation. Measured 7LiH backgrounds are listedin Table III.

C. Thermal Activations of LIH

The test samples of lithium hydride irradiated inthe thermal flux contained a low concentration of CLi(about 0.1%) to limit perturbation of the neutronflux by absorption in the sample. Even so, the ‘Liand ‘H in the samples produced a combined fluxdepression, with approximately equal contributions,of about 5Y0, a depression for which we could ade-quately correct.

The gold fluence monitor obviously should havebeen uniformly distributed in the sample, but wefound no way to do this. Gold powder settled quickly

2.2761.944

TABLE III

RatioT/NBS

0.99601.0083

TRITIUM ACIYVITY IN UNIRRADIATED

AMPULES OF ‘LiH

Mass 7LiH ‘Ihitium Decay RateSample No. (g) [dis*s-’”(gLiH)-l]

125127128179176182189190316322323

0.14670.15890.16941.01251.00690.95011.00281.00270.89821.06831.0871

2.3174.9003.2502.7502.6673.2603.6003.5163.5838.6173.lm

av = 3.78 + 0.52

to the bottom of the ampule, and the use of solutionspromised to add more problems than it solved. Ineach ampule we placed a sample of approximately10 mg of 0.05-mm-diam gold wire wound in a helixon a 1.6-mm-diam mandrel. The helix was stretchedaxially to span the inside diameter of the ampule(about 8 or 16 mm for the two sizes of ampules), andwe attempted ta locate the helix along the axis of thefill tube. X-radiographs of the filled ampules showedthat not all helixes were collinear with the fill tube,but we judged consequent errorsin fluence measure-ment to be negligible.

, 7

D. Gamma-Ray Counting of ‘e’Au

We counted the 412-keV gamma rays from the ac-tivated gold in the samples with a Ge(Li) detector.To eliminate small errors in ampule shapes andplacements, each sample was rotated at 0.1 rev/swhile it was counted. The sample holder wasmounted rigidly and reproducibly by a clamparound the case of the Ge(Li) detector, as shown inFig. 8. We calibrated the gamma-ray detector byplacing standard sources in the same samplemounting. One standard source* was 152Eu,whichhas, by coincidence, a 412-keV line. A second stan-dard source was a few milligrams of activated goldwire that LASL radiochemists (Group CNC-11)counted in a NaI(Tl) well detector and also with a

●Purchased from Laboratoire de M6trologie des RayonnementaIonisants, Commissariats a l’Energie Atomique, Saclay, France.

dN2

~ “ ‘1NAuU2$- A2N2 , (2)

where K1 is the ratio of neutron fluence averagedover the length of gold wire to that averaged overt hevolume of lithium hydride (see Appendix B for thiscalculation); a is the thermal capture cross sectionof gold; and AXis the decay constant of lqlAu. Thesolutions of these equations for an irradiationstarting at t = O and ending at t = t. are

Nl(te) = NLi-6CJ1[l - exp(-~lte) ]l$l/X1 (3)

N2(te) = K1NAUIJ2[1- exp(-k2te) ]1$/A2 , (4)

and these give

ual -‘Li-6 1 2 exp (-A1te)Nl (t=) = N2(te) NAUU2X1 1 - exp (-A2te) “ (5)

Ge(Li) detector. Both of these counters werecalibrated with a NBS mixed radionuclide emissionrate standard.

E. Calculation of Expected Tritium Activity

To determine the relation between the predictedtritium decay rate dNJdt and the number of ‘98Augamma rays counted, we note that the net produc-tion rate of tritium is

where al is the thermal cross section for ‘Li(n,a), AIis the decay constant for tritium, and I#Jis the ther-mal neutron fluence averaged over the volume of theampule. Likewise, the net production rate for lUIAUis

Fig. 8.Rotating sample holder mounted on the Ge(Li)detector that was used to detect the 412-keVgamma rays from test samples activated bythermal neutrons.

We determined N,(tJ, the number of ISSAUatomsat the end of the irradiation, by “counting the 412-keV gamma rays with a Ge(Li) detector of efficiencye. The number of ‘g8Audisintegrations per second inthe interval At starting at elapsed time t, after the

8

end of the reactor irradiation was determined fromD, the number of 412-keV gamma rays detected, us-ing the relation

where(1)

(2)

(3)

(6)

T is the measured transmissionof the 412-keVgamma rays through the LiH sample andquartz wall;the constant /3 is a combination of thebranching ratio and internal conversion coef-ficient in the decay of “Au; there are @ 412-keV gamma rays per disintegration;K, is a coefficient that relates to the size of thegold wire used to measure neutron fluence(some neutrons entering the gold wire andgamma rays leaving the wire are absorbed).

In Appendix C we calculate KZ, the ratio of the frac-tion of gamma rays escaping the gold to the limitingvalue for an infinitely thin wire. Now

E(tl, At) - N2(te) exp(-A2t1) [1 - exp(-X2At) ] ,

(7)

where we have accounted for ‘BEAudecay duringelapsed time ti starting at time t. and also for decayduring the counting interval At. From Eqs. (6) and(7),

D exp(lztl)‘z(te~ = TCBK2[I - exp(-~2At)1

and substituting for NZ [Eq.

9 (8)

(5)] we get for thenumber of tritium atoms formed in terms of thenumber of 412-keV gamma rays detected,

N = ‘Li-6”lA2’1 - ‘m ‘-Alte) ]1 NAuu2~l [1 - exp (-A2te) 1

D e.xp(A2t1)

“ Te8KlK2[1 - exp(-A2At) J “ (9)

The mass of lithium per gram of LiH, g, was deter-mined by Union Carbide’s analysis of the material.T%e numbers Nu., and NAUof lithium and goldatoms are given by

and

A.—~‘Au ‘Au 2’

(lo)

(11)

where AL1and AA. are the atomic weights (for theisotopic mixtures as used) of the lithium and gold, Ais Avogadro’s number, and f is the isotopic abun-dance of ‘Li. The number of tritons formed per unitmass of LiH is then

‘1 a1A2g_=%. ,

fD exp(A2t1)

5 %1 “2A1”2 Te 6K1K2

1- exp (-Alte)

“[l-(12)

e.xp(-12te)1[1 - exp(-A2@ 1 “

To compare calculated and measured tritiumcounting rates, we determined the decay rate perunit mass of LIH:

AAuu1k2gf [1 - exp(-A1te)1 D em (a2tl)~iu2rn2[l - em (-k2te) 1[1 - exp(-a2At) ]TeBK1K2 “

(13)

The constants appearing in Eqs. (12) and (13) havethe values given below.

Conetant value

196.W

7.01606936*4b98.8 + 0.3 b1.7781x 10-’ S-12.976x 10-’ s-’0.670750.9447 (large ampulea)0.9710 (small ampules)3.9611 x 10-’0.95479.42 X 10-’

1.005 (small ampules)1.013 (large ampules)O.aaao

Reference

CRC Handbook of Chemist~and Physicu, 56th ed.(calculated)891011Union Carbide(meaaurad)(measured)(measured)12Union Carbide and LASLanalysesAppendix BAppendix BAppendix C

9

Table IV, which gives the predicted [from Eq.(13)] and the measured tritium activities for thelithium hydride samples irradiated by thermalneutrons, shows that predicted-to-calculated ratioshave values characteristic of the size of the sample.Table V summarizes this dependence and shows alsothe ratios of predicted and measured volumes ofevolved gas. The fact that these have similarsystematic variations suggesta that most of thesystematic error in Teledyne’s tritium measurementis characteristic of the process of gas evolution andconversion to water. Using the thermal fluencetritium-production measurements to establish stan-dards, we normalized the tritium determinationresults from Teledyne for the small and large sam-ples by the divisors (from Table V) 1.103 and 1.058,respectively. If we note that Teledyne’s quoted

systematic error for the entire proceiw was 5Y0,wefind these normalizations quite plausible.

We adduce an additional piece of evidence thatsupports the assumption that the systematic errorinthe Teledyne measurement is characteristic of thesample processing. Teledyne measured the tritiumdecay in sample 305, which contained 0.1594 g ofLiH, with 0.1 at.% CLi.This was one of the test sam-ples irradiated in thermal neutron flux. This samplewas converted to gas and additional hydrogen carriergas was added in a manner typical of all small am-pules. The total volume was then converted towater; an aliquot of this sample was converted backto hydrogen and counted in a gas proportionalcounter with a resulting activity of347.15dis OS-’o (g H,O)-’ as of 24 June 1976,Anotheraliquot of the water from this sample was certified

TABLE IV

TRITIUM ACTIVITY INDUCED BY THERMAL NEUTRON IRIMDIATION

Sample No.

Mass ZiH,

:)

302305307309312313

31531932132632a

0.13840.15940.16550.15980.14960.1682

0.87890.92691.04840.92910.9232

l?ritium Counting Rate,”nr,l odNr/dt

[10’ counts ”s-’”(g LiH)-’]

Predicted Measured

2.205 2.3622.165 2.5282.135 2.3622.067 2.2122.271 2.5282.150 2.345

2.223 2.4282.180 2.2622.319 2.4622.117 2.1912.283 2.428

RatioMeasured/Predicted

1.0711.1681.1061.0701.1131.091

av = 1.103* 0.015

1.0921.0381.0621.0351.064

av = 1.058+ O.O1O

‘Ae meaeuredby Teledyne and as predicted from the gold activation. Fractional ‘Li abundance was9.42 x 10-’. Reference time was 1200 MST, 26 February 1976.

,.

. .

10

TABLE V

RATIOS OF MEASURED-TO-PREDICTEDVALUES FOR VOLUMES AND

ACTIVITIES OF EVOLVED GASES

Average Ratio Measured-to-Sample of Volume Predicted Tritium

size H2” Activityb

Small 1.0257 + 0.005 1.103 * 0.015Large 0.9519 & 0.015 1.058 + 0,010

‘Predicted values were obtained from LiH mass and the UnionCarbide reported value for the number of grame of H, per gram ofLiH.

b%edicted valuea are derived from thermal activations (see TableIv).

by NBS to have an activity of 315.5 + 6 dis. s-’.(g H,O)” as of 24 June 1976. (The uncertainty of 6s-is g-l is the linear sum of 1.3, the random error at99% confidence level, and 4.7, the linear sum of con-ceivable systematic errore.) The ratio of these twomeasurements is 1.1003, consistent with the correc-tion factor (see Table IV) determined by the gold-monitored thermal activations of the small samples.We have already seen (Table II) that Teledyne andNBS determinations of tritium activities in two frac-tions of a sample of tritiated water agree within 1.5Y.(which is expected because both determinations arereferred to as the same standard sample) so thesystematic error is probably characteristic ofTeledyne’s gas handling system.

IV. TRITIUM-PRODUCTION RESULTS

The neutron production from the T(d,n) reactionin the target inside the aLiD assembly wa5

monitored by counting the alpha particles from thetarget in a small solid angle at 135° with respect tothe deuteron beam direction. The total number ofsource neutrons produced was (9.42 + 0.28) x 1016.Additional data on the total number of neutronsand the change in their energy spectrum as theywere transported through the ‘LiD assembly wereacquired by the LASL Radiochemistry Group, CNC-

11, through the use of various activation foils. Theseresultda appear in Part II; those obtained at the in-ner surface provide a measure of the 14-MeVneutron flux and are compatible with the alpha-particle monitor data.

The results of Teledyne’s analyses of the samplesof lithium hydride are given in Table VI. Intabulating the Teledyne counting data, we sub-tracted from their reported number of counts pergram of lithium hydride the same quantity for unex-posed samples. The backgrounds measured in ir-radiated ampules containing only helium werenegligibly small. We applied an additional correc-tion because Teledyne used 12.26 yr for the half-lifeof tritium in determining the activity as of 26Feburary 1976 from an NBS standard dated 3September 1961. The apparent best value for thetritium half-life is 12.35 yr (Ref. 10), implying thatTeledyne’s counting data should be multiplied by1.006.

The results for both lithium isotopes are plotted inFig. 9, along with the results of measurements byWyman.1 Although his measurements were made inan assembly of the deuteride of natural lithium, hisresults are nearly the same as those in this experi-ment.

The fractional standard deviation for data listedin Table VI is 6Y0.

To evaluate the systematic errorsin these tritium-production measurements, we assumed that thestandard deviations in the normalizations (thosefound for the measured-calculated ratios in TableV—1.5 and 1.0% for small and large ampules,respectively) are also systematic errors in thesedeterminations. The standard used to determine thecounter efficiency for the 412-keV gamma rays forgold had an error quoted by the Laboratoire deMetrologiesdes Rayonnements Ionisants as +2% at%ly. confidence level. We checked this sourceagainst a separate standard, used by radiochemistsat LASL, whose uncertainty was also quoted as +2Y0

at the 99% level. The two standards agreed to within

2Y0, and we used an average of the two, assigning a

2~0 systematic error. The standard deviation of ayo

in the neutron-source strength also appears as asystematic error. We used the linear sums of the er-rors to obtain total systematic errors of 6.5 and 6°%for small and large samples, respectively.

11

TABLE VI

RESULTS OF TRITIUM-PRODUCTION MEASUREMENTS

TritiumDecay Rate’[s-’*(g LiE)-’]Lacation

(seeFig. 4)Mnms

Normalised f(r)’Teledvne and 110-” atoms.mm*

Teledyne(U26176)

33.036.6746.0

226.3240.0240.0

.,

.,

Li SampleIoo@e No.— —

6 136137146

138139140

Lilr(6) (LA) (:;) “Ne@-

(2/26/76)(krrrectad” - “(Liatom)-’

(3/27/76) o(source neutron)-’]

1.1071.05441.0429

29%5299.5299.5

-:135

-15-3s

-145

-30-135

30

-5540

-464

–20120

–12635

-3030

136

–4055

-6046

31.23 24.6634,71 27.4142,69 33.63

216.1 77.240.94641.02131.0584

0.9963o.a6311.0939

0.14090.1218

0.14320.1367

0.90540.9128

0.s4320.9343

201.6201.6201.5

227.2227.2

81.2181.21

689.6662.1832.5

81.5079.0187.70

141142143

104111

127.5127.6125.5

601.7583.3868.3

10671086

77.6476.86

969988

51.4261.13

106110

7 1631s6

147173

17171883

17.1717.0

52.6769.33

15591526

36.8932.97

61.249.5

299.6289.5

13.3913.22

12.6712.51

11.3611.21

201.6199.5

47.8954.65

45.3361.83

18.3920.63

149 166.33171 166.7172 166.7

101 570.0114 666.7

103 1353108 1342

‘Isotopic abundances in the test samples were: ‘Li, 95.6034%; T& 99.9058%. MolecuIar weights used were ‘LiH, 7.066;7LIH, 8.023.

bPositive angles are below the parting plane in Fig. 4; negative angles are ahove.

‘Counting rate of evolved tritium.

%itium activities in %ii samples were corrected for a background measured in unirradiated samples of 3.78 + 0.52 s-’. (g LiH)-i (see Table III); ‘LiH samples had negligible background.

Teledyne counting data were corrected because they were based on a tritium half-life of 12.26 yr instead of the presentlyaccepted 12.35 yr; this affecta the NBS standard used (dated 9/3/61).

The specific tritium production, f(r), (equals 4+ times number of tritons formed per atom of lithium for one sourceneutron).

0.78920.90680.8788

0.14650.1211

0.13400.1303

184.6162.9162.9

166.8154.1164.1

25.3125.0325.03

127.5125.5125.5

77.6875.66

668.2562.9

514.0611.0

30.9626.23

49.561.6

13491338

12241215

29.9732.20

.

.ACKNOWLEDGMENTS Ridge, TN 37630, for fabrication of the ‘LID as-sembly and preparation of the LiH-filled ampules.

We are grateful ti the machine operators in LASL We especially thank J. David Martin at TeledyneGroup R-2 for operation of the C-W machine; to Isotopes, Westwood, NJ 07675, whose expertise inJames J. Bramble for design of the OLiDassembly; tritium measurements made this project possible.and to the staff at Union Carbide Corporation, Oak

12

Iooll I=I I I

.

oo~Im 200 300

RADIUS r (mm)

Fig. 9.ZYitium productwn in a sphere of ‘LiD plottedas f(r) = 41r? times tlw number of tritow peratom of lithium for one 14-MeV neutron at thecenter of the assembly. The triangles aremeasurements by Wymard of tritium produc-tion in 7Li metal embedded in a sphere of LiD.The circles are our ‘Li production data; thesquares, ‘Li data. The curves are drawn toguide the eye.

——— ———— ——— ——— ——— —____

APPENDIX A

TRITIUM DECAY RATES IN SAMPLES OF UNIRRADIATED 7LiD

Tritium decay rates in samples of 7LiD prepared TABLE A-Iby Union Carbide Corporation are listed in TableA-I. BACKGROUNDS IN ‘IAD SAMPLESa

SampleNo.

6569

107108109110111

Mass LiD

(!?0

0.17330.20%1.10781.13971.02850.96811.0162

Activity[10’ counts ”s-’” (g LID)-’]

1.638“ 1.138

1.3171.3171.2991.2421.221

av = 1.310 + 0.060

“Ae of 1 July 1975. The atomic abundance of %i was 1.047 x 10-4.

13

CALCULATION

To find a value for the thermal

APPENDIX B

OF VOLUME-AVERAGED

neutron fluenceaveraged over the volume of lithium hydride in aquartz ampule, we must take account of the at-tenuation of flux as it passes through the lithiumhydride itself. These types of calculations have beendone for purely absorbing media by Case, de Hoff-mann, and Placzeki’ for several different geometries.For a sphere of radius a immersed in an isotropicbath of monoenergetic neutrons, the average fluxthroughout the volume relative to that far away isgiven by

PO=+; (?‘< ‘) ‘

where 1?is the absorption mean free path. For asphere of lithium hydride [(9.42x 10-2)% CLi]with a= 8.0 mm and.4 = 257.9 mm, a/,C= 0.0310 and PO=0.9767. Thus the fluence averaged over the sphere isonly a few per cent different from the fluence faraway. This difference is an upper limit of the correc-tion necessary because the gold was distributedalong a diameter and not throughout the volume.

If o(r) represents the radial distribution ofneutrons in the sphere, then the average fluence in-teracting with the lithium hydride is given by

a

TV= 31a3J f$(r)r2 dr ,

0

NEUTRON FLUENCE

and the fluence averaged along a radius is given by

a

7= - Ila J_$(r) dr .

-o

With the gold wire positioned along a diameter ofthe ampule, we determined & by counting thenumber of 412-keV gamma rays.

We used the code DTF-IV (Ref. 15) to estimateO,(r) in one-group S. calculations with n = 8, aasum-ing isotropic scattering in the center of mass.Calculations were performed using both purely ab-sorbing media and with several different estimatesof the scattering cross section for lithium hydridemolecules. Neutron interactions in the quartz am-pules were also included in the calculations. Wecalculate that the ratio of the averaged fluxes,

is 1.005 + 0.002 for the small ampules and 1.013 +0.005 for the large ones. This relation was used tocompute the amount of tritium produced in the twodifferent size ampules.

APPENDIX C

NEUTRON AND GAMMA-RAY ABSORPTION IN GOLD WIRE

.*

. .

.

0

A 0.05-mm-diam gold wire in the form of a helix in a fluence lower than that at the outside of thewas positioned along the diameter of the ampule to wire. Furthermore, some of the 412-keV gamma raysmeasure the thermal neutron fluence within the test originating in the interior of the wire fail to escape.samples of LiH. Gold has a sufficiently large neutron These effects are smaller than 5%, and we calculatedcapture cross section that the interior of the wire is the correction for them.

14

*.

. .

We assume that the pitch of the gold helix is greatenough—perhaps 50 wire diameters—that we canmake the calculation for an infinite straight wire.The calculations for neutrons entering and gammarays leaving are identical. We refer to the calculationof average fluence by K. M. Case, F. de Hoffmann,G. Placzek14for a purely absorbing medium. Theircalculation is appropriate for gold, which has a crosssection for absorption 10 times greater than that forscattering. For radii small compared to the meanfree path, they find for the escape or entranceprobability,

——.——— ————

REFERENCES

1.

2.

3.

4.

5.

Marvin E. Wyman, “An Integral Experiment toMeasure the Tritium Production from ‘Li by 14-MeV Neutrons in a Lithium Deuteride Sphere,”Los Alamos Scientific Laboratory report LA-2234, Rev. (November 1972).

R. Herzing, L. Kuijpers, P. Cloth, D. Filges, R.Hecker, and N. Kirch, “Experimental andTheoretical Investigations of Tritium Produc-tion in a Controlled Thermonuclear ReactorBlanket Model,” Nucl. Sci. Eng. 60,169 (1976).

Lambert J. M. Kuijpers, “Experimental ModelStudies for a Fusion Reactor Blanket,” thesis,Technische Hogeschool, Eindhoven,Netherlands (1976).

H. Bachmann, V. Fritscher, F, W. Kappler, D.Rusch, H. Werle, and H. W. Wiese, “NeutronSpectra and Tritium Production Measurementsin a Lithium Sphere to Check Fusion ReactorBlanket Calculations,” Nucl. Sci. Eng. 67, 74(1978).

D. W. Muir and M. Wyman, “NeutronicAnalyses of a Tritium Production Integral Ex-pediment,” Tex. Symp. Technol. CTR Exp.November 20-22, 1972, Austin, Texas (1972).

H+w’”’($)+w)%-’) ‘Po= l-–

where Euler’s constant ~ = 0.577216.For gold the capture cross section of 98.8 b gives a

mean free path A of 1.715mm. For radius a = 0.0254mm, a/& = 0.01481and, from the above equation, PO= 0.9809.

For the gold gamma ray, cab. = 62 b, which gives amean free path 12 = 2.733 mm. Then a/.% = 0.00929and P, = 0.9879.

The product of the entrance and escapeprobabilities is the constant, KZ = 0.9690, used inEq. (6).

,—_— —_ —— __

6.

7.

8.

9.

10.

11.

12.

13.

S. M. Qaim, R. WNfle, and G. Stocklin,“Nuclear Data for Fusion Reactors, ” ATOMKIKozl. 18, 335 (1976)

S. M. Qaim, R. Wolfle, and G. Stocklin,“Radiochemical Methods in the Determinationof Nuclear Data for Fusion ReactorTechnology,” J. Radioanal. Chem. 30,35 (1976).

Norman Holden, National Neutron Cross Sec-tion Center, Brookhaven National Laboratory,Upton, NY 11973,private communication, 1976.

S. F. Mughabghab and D. I. Garber, “NeutronCross Sections, Resonance Parameters, ”Brookhaven National Laboratory report BNL-325 (1973) Vol. 1, p. 79.

M. J. Martin and P. H. Blichert-Toft, “Radioact-ive Atoms,” Nucl. Data Tables 8, 14 (1970).

M. J. Martin and P. H. Blichert-Toft, “Radioac-tive Atoms,” Nucl. Data Tables 8, 153 (1970).

Ronald L. Auble, Nuclear Data Group, OakRidge National Laboratory, Oak Ridge, TN37830, private communication, 1976.

Donald W. Barr, Los Alamos ScientificLaboratory Group CNC-11, private communica-tion, 1976.

15

14. K. M. Case, F. de Hoffmann, and G. Placzek, 15. Kaye D. Lathrop, “D’I’F-IV, a FORTRAN-IV“Introduction to the Theory of Neutron Diffu- Program for Solving the Multigroup Transportsion,” (Los Alamos ScientWlc Laboratory, Los Equation with Anisotropic Scattering,” LosAlamos, NM 87545, 1953), Vol. I. Alamos Scientific Laboratory report LA-3373

(November 1985).

. .

. .

.

.

16

PART II

CALCULATIONS OF TRITIUM PRODUCTION ANDRADIOCHEMICAL ACTIVATION IN A SPHERE OF

aLiD IRRADIATED BY 14-MeV NEUTRONS

by

Jon M. Wallace

.

ABSTRACT

The SPCCWICproduction of tritium in ‘LiH and 7LiH embedded ampules and

the activation of radlochemical detector foils of %3c, 89Y,‘Zr, 10%, 19%.87910gIr.,2,,lnAu, ‘a’U, and 28SUplaced at various positions in a 600-mm-diam‘LiD sphere irradiated by a central source of 14-MeV neutrons have beencalculated and compared with experimental data. One- and three-dimensional Monte Carlo and S. neutron-transport calculations were per-formed. The most reliable (three-dimensional Monte Carlo) calculationgenerally agrees with both the tritium-production and the radiochemical-activation data. The existing discrepancies between calculation and experi-ment appear largely attributable to uncertainties inproduction and radiochemical-activation cross sections.

some tritium-

1. INTRODUCTION

We present the results ofcalculations in a 600-mm-diam

neutron-transportsphere of OLiDir-

radiated by a central 14-MeV neutron source.Tritium production from lithium in embedded aLiHand 7L1Hampules and the neutron-induced activa-tion of radiochemical detector foils placed at variouspositions in the sphere were obtained and comparedwith experimental data. The ‘LiD sphere, theneutron source, and the tritium-productionmeasurements have been described in detail in PartI of this report. Additional diagnostic informationwas obtained from six radiochemical foil packetsplaced at the interfaces of the concentric ‘LiDspherical assembly. The foil materialswere‘“SC, ‘SY,‘Zr, l’~m, “’Ir.,,, ‘%.,,,, “’Au, “W, and ‘“”U. Thefoils were analyzed by radiochemical methods afterthe irradiation.

The comparison of our calculations with the in-tegral experiment provides a simultaneous test of

the neutron-transport codes, the neutron cross-section data relevant to transport through ‘LiD, thetritium-production cross-section data, and theradiochemical-activation cross-section data.

II. CALCULATIONS

Four different calculations of this experiment willbe discussed. They vary in reliability, and their in-tercomparison is instructive because it points outthe shortcomings of the less accurate calculations.Each calculation consisted of two parts: (1) aneutron-transport computation to produce fluences,that is time-integrated fluxes, at various detectorpositions, and (2) an evaluation of theradiochemical-activation integrals and, for Calcula-tions I-III, the tritium-production integrals for com- 1

parison with the experimental values. In CalculationIV, the tritium production was obtained directly inthe neutron-transport computation. The ‘Li and 7Li

I17

I

cross-section data used in both the transport andtritium-production computations were ENDF/B-IILThe 1967 United KingdomfLASL evaluation of thedeuterium cross sections was employed in the tran-sport computation. The radiochemical-activationcross sections used were from the LASL TD-DivisionDosimetry Library.* The (n,f) and (n,~) cross sec-tions in this library werenormalized using BIG 10**data. There is a 3% normalization uncertainty in ourresults that is due to the uncertainty in the numberof 14-MeV source neutrons, as described in Part I ofthis report. The calculations will now be discussed inorder of increasing reliability.

A. Calculation I—lD, 1l-Group, S,,P1

In this calculation the neutron fluences at the re-quired radial distances from the source were com-puted using a one-dimensional neutron transportcode with n-group, St,Pl neutron transport. Thegroup structure is given in Table I. The sourceneutrons were distributed between 13.5 and 17.0MeV according to an appropriate weighting func-tion. The radiochemical-activation and tritium-production integrals were computed with cross sec-tions collapsed into the n-group structure using thesame weighting function.

B. Calculation II—ID, 21-Group, S8,P1

This calculation is similar to Calculation I, exceptsmaller energy and angle bins are used in a 21-group,S,P, transport scheme. The energy group structure isgiven in Table II. In this computation, group 1 isempty. The source neutrons were distributedbetween 13.5 and 15.0 MeV according to theweighting function used in Calculation L As in

*The Sc(n,-y) cross sections are based on ENDF/B-IV, DosimetryLibrary. The Y(n,y) cross sections were taken from an evaluationby E. D. Arthur in “Applied Nuclear Data Research and Develop-merit, ”LASL report LA-6971-PR (September 1977) (compiled byC. I. Baxman and P. G. Young), p. 3. The Tm(n,y) cross sectionsare from a private file of J. S. Hendricks. The (n,2n) cross sec-tions, except for ‘“U, were taken from evaluations based on datain B. P. Bayhurat, Phys. Rev. C 12, 451 (1975). All other activa-tion cross sections were based on ENDL (Llvermore EvaluatedNuclear Data) 4/76.

**BIG 10 is a critical assembly at LASL.

TABLE I

ENERGY GROUP STRUCTURE FORCALCULATION I

GroupNumber

JL.ow.(MeV)

123456789

1011

13.510.07.793.682.2320.5000.1840.02480.003350.0001670.139 x 10-9

EM-X= 17.0

Calculation I, this weighting function was also usedto collapse the radiochemical-activation andtritium-production cross sections into the 21-groupstructure.

C. Calculation 111—lD, Monte Carlo

In this calculation the neutron fluences at the re-quired radial distances from the source were com-puted using the three-dimensional Monte Carloneutron-transport code MCN.aIsA one-dimensionalmockup of the spherical assembly, similar to that inCalculations I and II, was used. The fluences, whichwere surface integrated, were binned into a 75-groupstructure (Table III). The point-source neutronswere distributed isotropically with energy 14.1 MeV.Radiochemical-activation and tritium-productionintegrals were calculated using precollapsed crosssections and the 75-group histogram fluences. Thefluences in the high-energy range relevant to the(n,2n) activations were increased by 2% to simulatethe effect of the observed source anisotropy in thedirection of the radiochemical detectors. This is ourmost reliable one-dimensional calculation. The rele-vant geometric parameters for Calculations I-III aregiven in Table IV.

.,

.,

.

,

18

TABLE II

ENERGY GROUP STRUCTURE

FOR CALCULATION II

GroupNumber

&ower

(MeV)

1

23456789

101112131415161718192021

15.013.612.010.07.796.073.682.8652.2321.7831.3630.8230.6000.3030.1840.06760.02480.009120.003360.0001670.139 x 10-’

EM.. = 17.0

TABLE 111

ENERGY GROUP BOUNDARIES

FOR BINNING INCALCULATIONS 111AND IV

16.22MeV’15.12”15.00”14.87”14.75’14.62”14.50”14.37”14.25’ 14.llb14.12’ 14.05b14.0013.8713.7513.6213.5013.3713.2513.1213.0012.8312.6712.50

12.3312.1612.0011.7511.5011.2511.0010.7510.6010.2510.009.759.509.259.008.758.508.167.797.407.006.75

6.606.286.075.785.505.265.004.754.504.093.683.272.8652.552.2322.0001.7381.5501.3531.0900.8230.660

0.5000.4000.3030.2440.1840.1250.06760.04600.02480.01700.009120.006000.003350.0012350.0004540.000167o.m14O.0000

‘Energy boundaries for Calculation lV,

Wnergy boundaries for Calculation III,

TABLE IV

GEOMETRICAL DATA FORCALCULATIONS I-III

OutsideRadius Density

(mm) Material (g/cm’)

22.250.051.076.1577.15

126.0127.0200.0201.0300.0

0.00.7530.00.7630.00.7530.00.7510.00.755

19

D. Calculation IV—3D, Monte Carlo

The neutron fluences in this calculation also wereobtained using MCN. The calculation incorporateda simplified three-dimensional mockup of thespherical assembly, including small spherical ‘LiHand 7LiH regions to simulate the tritium collectionampules. The geometric data are given in Table V.The geometry is illustrated in Fig. 1. Tritiumproduction was calculated on-line by the neutron-transport code. Neutron fluences for theradiochemical-activation integrals were tallied atthe points where the detectors were located forneutron energies >7.40 MeV. Surface integratedfluences, as in the one-dimensional calculations,were used for energies E z 7.40 MeV. This hybridtreatment was employed because the MCN point-fluence tally is very time consuming. The tallyshould not be necessary at lower energies becausethe multiple-scattering process, which produces the

TABLE V

GEOMETRICAL DATA FORCALCULATION IV’

DensityMaterial (g/cms)

aLi.s~6~7Li.0~~~D 0.7425Stainless steel (SS) 9.03LiH

Distance of CenterFrom Source

(mm)

0,300

Radius of LiH Spheres

Experiment(mm)

Calculation(mm)

50.576.65

126.5200.5

300.0

5.05.0

9.09.0

9.0

5.06.0 ‘LiH5.5 lLiH9.09.0 ‘LiH

12.07LiH15.3

“Source volume: spherical region of radius 2.0 mm.

20

Fig. 1.The geornetqy of the ‘LiD sphere used inCalculation IV. The small embedded LiHspheres are not shown, but are located at thepositions illustrated in Fig. 4 of Part I of thisreport. The radii of the LiH spheres in thecalculation are in some cases larger than theradii of the ampules used in the ezpen”ment(Table V).

lower energy component of the neutron spectra,tends to produce an isotropic distribution as theneutrons are downscattered. For this calculation,the fluences were binned into an 83-group structure(Table III), which consisted essentially of the groupstructure of Calculation III with eight additionalgroups at the upper energy end. The calculationemployed an anisotropic energy-angle correlatedsource occupying a spherical volume, which closelysimulated the experimental source (see Fig. 3 of PartI of this report). The energy-angle correlation is thatproduced by a 240-keV deuteron beam on a tritiumtarget.* The radiochemical activations were ob-tained just as in Calculation III, using the histogramfluences. Of the four calculations, this one is the

*For this calculation, this correlation is identical to that for the300-keV beam actually used in the experiment.

most precise simulation of the experiment. Com-parison of the results of this calculation with the ex-perimental data provides the best test of how well weunderstand the processes under consideration.

III. TRITIUM PRODUCTION

The experimental tritium-production results ateach radius have been averaged for comparison withthe calculations. This average is the proper com-parison for Calculations I-III, which are sphericallysymmetric, and provides better statistics for com-parison with Calculation IV. In addition, thetritium-production results are compared ampule byampule with the results of Calculation IV.

All comparisons are made in terms of the ratio ofthe experimental results to the calculated results.The quoted uncertainties for this ratio are from theexperimental uncertainties only.

A. Tritium Production From ‘Li

The material contained in the ampules was‘Li.SOw,8‘Li.,m,2 H. So the quantity observed was

‘~i-’ = 4nr2[00’’’8~0,(E)uL,L7(E)E) ‘E

+ 0.000942J 1I$i(E)uLi_6(E) dE s

where (hi.1 is the reaction cross section for 7Li(n,n’a)and ~IJ.@is the reaction cross section for ‘%i(n,a).

Here O, is the neutron fluence spatially integratedover the ampule volume. The amount of tritiumproduced from ‘Li is never more than 0.3% of thetotal. The ‘L1 tritium-production reaction thresholdis at 2.8 MeV; thus these data probe neutron tran-sport only in the energy range above this threshold.

The results of the calculations are presented inTables VI and VII and shown in Fig. 2. The variouscalculations differ from each other by as much as‘zs~. at the 300.O-mmradius (at the outside of theLID sphere) with typically 10% differences at theother positions. All calculations give overpredictionsat the inner three positions. Calculation IV gives thebest overall agreement with experiment, the dis-crepancies being generally smaller at positionsfurther away from the source. These results aresimilar to those of a recent analysis of the Wymanexperiment.4-6In Sees. lV.A and IV.B we discuss(n,2n) and (n,f) activations of ‘W, in which there isgenerally good agreement between calculation andexperiment. The cross sections for these two reac-tions are qualitatively similar to the 7Li tritium-production cross section and are thought to berelatively well known. Hence it is not unreasonableto attribute the 7Li discrepancies to the tritium-production cross section used. A 15% reduction ofthe cross section in the 14-MeV region would bring

TABLE VI

RATIO OF OBSERVED-TO-CALCULATED TRITIUM PRODUCI’ION FROM ‘Li

Distance FromSoum% Average Experimental Result(mm) (10-” atoms ”mm’/Li atom)

50.5 31.0976.65 30.10

126.5 25.12200.5 19.46300.0 11.29

‘Ratio of experiment to calculation.

Calculation’

I II III IV—. —.

0.783 0.836 0.873 0.8830.811 0.838 0.882 0.8610.834 0.809 0.860 0.8900.989 0.883 0.926 0.9181.266 1.024 1.015 0.986

TABLE VII

CALCULATION IV AND OBSERVED TRITIUM PRODUCTION FROM ‘Li

SampleNo.

109

103114101171149172173147183

DistanceFrom Source

(mm)Observation

(10-” atoms”mm’/Li atom)Calculation IV

(10-” atoms ”mm’fLi atom)

50.5

76.65

126.5

200.5

300.0

32.2029.9729.2330.9625.0325.3125.0320.5318.3911.3611.21“

35.634.835.534.4223.329.526.921.121.312.010.9

the calculation into significantly better agreementwith the experiment.

B. Tritium Production From ‘Li

The material contained in the ampules was7Li.,,,M,‘L1.,,,,,, H; so the observed quantity was

186

TRITIUM PROWCTION FRCM h

I

..,~0 !s0 1001s02002!s0300

RADIUS (mm)

Fig. 2.Ratio of observed-to-calculated tritiumproduction from ‘Li us radius. The error barsare from random experimental uncertaintiesonly. There is an additional normalization un-certainty of -3%.

‘~-’ = 4nr2k-044’’’~$,’E)UL7(E)E) “

+ 0.955034J 1

I$i(E)oLi_6 W “ .

The 7Licontributes no more than -5”A of the tritiumproduced in these ampules, with the largest frac-tional contributions generally occurring in the am-pules closest to the source. The cross section fortritium production from ‘Li is reasonably wellknown. It has a general decrease with energy, with aresonance superimposed at 240-keV neutron energy.Most of the tritium production arises from neutronenergies around and below this resonance energy.

22

TABLE VIII

RATIO OF OBSERVED-TO-CALCULATED TRITIUM PRODUCTION FROM OLi

Calculation”Distance

From Source Average Experimental Results(mm) (10-’” at~m~ .mm’/Li a~m) I II III Iv

—— ——

50.5 34.48 0.877 1.020 1.089 1.03976.65 51.28 0.840 0.953 1.029 0.863

126.5 82.74 1.006 1.086 1.187 1.087200.5 79.89 1.071 1.074 1,179 1.014300.0 28,57 1.W9 1.213 1.441 0.963

‘Ratio of experiment to calculation.

bAmpule density p = 0.3041g/cm’.

TABLE IX

CALCULATION IV AND OBSERVED TRITIUM PRODUCTION FROM ‘Li

DistanceSample From Sourca Observation Calculation IV

No. (mm) (10-’4 atoms .mm’/Li atom) (lO-U atoms ”mm2/Liatom)

110 50.6106111 76.65104143 126.5141142138 200.5139140136 300.0137145

32.9735.9951.1351.4287.7081.5079.0177.2481.2181.2124.6627.4133.63

33.033.459.159.775.579.373.581.576.078.730.330.6243.1

.

Resonance self-shielding is significant here, because in Fig. 3. The various calculations differ from each. strong contributions come from the region of the other by 15 to 25%. As for 7LI, Calculation IV gives

resulting dip in the neutron spectra. Comparison the best overall agreement with experiment. Anwith the ‘Li tritium-production data provides a anomalously large discrepancy occurs at the radialmuch more stringent test of our calculational source distance of 76.65 mm, for reasons unknown.capability than comparison with the 7Li data. The three-dimensional calculation gives a

The results of the various calculations are pre- significantly different radial dependence of thesented in Tables VIII and IX and shown graphically

23

1.3 I I I I I I

1.2– TRITIuM FRXXJCTKN FXN %1

1.1–

1.0– 1~~

1:09 –

IA

0.8 —

0.7 I I I 1 I Io 50 100 150 200 230 3~

RADIUS (mm)

Fig. 3.

Ratio of observed-to-calculated tritiumproduction from 6Li us radius. The error barsare from random experimental uncertaintiesonly. There is an additiorud normalization un-certainty of -370.

tritium production at this point than do the one-dimensional calculations. At all other radii, Calcula-tion IV is in rather good agreement with the experi-ment. Tritium production from ‘Li was quite sen-sitive to small changes in the device geometry,probably caused, at least partially, by resonanceself-shielding. For example, there is a surprisinglylarge sensitivity just to changes in the density of thesmall LiH collection spheres. Changing the densityfrom 0.30 to 0.50 glcma induces changes in thetritium production by as much as 10% in the largerLiH collection spheres. Given this high sensitivitytogether with the simplifications used in the MonteCarlo simulation of the experiment, we cannotreasonably expect much closer agreement betweencalculation and experiment than was obtained.

IV. RADIOCHEMICAL ACTIVATION

Three classes of activation reactions were con-sidered: (n,2n), (n,f), and (n,~). The (n,n’) activa-tion of I’iIr was also observed. The targets were “SC,““Y, ‘Zr, ‘a’Tm, ‘s’Ir.,,, ‘%.,,,, “’Au, ‘*KU,and “W.

The foil packets were placed in the plane perpen-dicular to the horizontal deuteron beam and 60° upfrom the horizontal axis, @ = 60° and 6 = 90° in thecoordinate system of Part L The foil distances fromthe source were 22.2, 60.0, 76.15, 126.0, 200.0, and300.0 mm. The foils were sufficiently thin that theydid not significantly effect the neutron flux in the‘LiD assembly.

The observed quantities are

where Ujis the activation reaction cross section forreaction j and 41 is the neutron fluence at the foilposition i. The data for this part of the experiment’are given in Table X. As in the presentation oft hetritium-production results, the results of the activa-tion calculations are given as the ratio of the experi-ment to calculation and the quoted errorsare due tothe experimental uncertainties only.

A. The (n,2n) Activations

The (n,2n) activations of six different targets wereobserved. The (n,2n) reactions considered here havethreshold energies ranging from -8 to 12 MeV, ex-cept for ‘“aU, which has a threshold of 6.17 MeV.These activations consequently result largely fromthe unattenuated 14-MeV component of the neutronspectra at the various radii. Comparison of thecalculations with the measurements provides a testof how well the transport codes treat 14-MeVneutron attenuation.

In Table XI, we give the “Y(n,2n) activationresults for the four calculations, which are typical ofall the (n,2n) results. Table XII gives the results ofCalculation IV for all activations. These results areshown in Figs. 4-10. From Table XI, we see thatthere is generally good agreement between the ex-periment and the two Monte Carlo calculations. TheS. calculations give less satisfactory agreement withthe experiment. This is due in part to streaming ef-fects in the S“ method, which does not permitprecisely radial transport. The large discrepancies atthe smallest radial source distance (22.2 mm), whichoccur in all the calculations, are thought to comefrom a slightly off-center source. The neutron

.,

.,

.

.

24

Reaction

8eY(n,2n)ooY‘Zr(n,2n)0sZr1’Wm(n,2n)1~mW.r(n,2n) l%‘nAu(n, 2n)‘WAU‘WJ(n,2n)n7UWr(n,2n)lwIr

+ Wr(n,~)iwIrlw~(n,n,)lwrnfi

2’W(n,f)wMo“’U(n,f)wMo‘6Sc(n,~)%3c‘“Y(n,~)wY‘e~m(n,~) ‘7’Tm‘WAu(n,~)lwAu‘aW(n,~)gaOU

TABLE X

RADIOCHEMICAL-ACTIVATION DATA” (10’*)

Distance From Source

22.2mm 50.0 mm 76.15 mm 126.0mm 200.0 mm 300.0mm

1665

39161540

2285

4.592

72.3546.11

219.2145.0528.6534.7578.3295.9401.1

61 + 15%829369

3.5082.029

59.8050.6329.75

76.2549.78

197.4197.6214.8118.7166.8

33 + 25%374150

2.4921.310

44.7536.4420.87

18.0211.4455.0051.1556.8837.1352.30

15 + so~o

14246.7

1.3630.8887

24.3819.8111.14

3.9992.131+4%

13.6212.7013.8710.8816.20

8 + 100%46.013.0k 4%0.55110.2562

10.048.1264.476

0.69240.3561+ g~o

2.9352.660 + 7yo

2.994

2.733 + 5’%.

2.97 + 7’%.

8.62+4%3.26+ 5%0.0971+ ‘7~o

0.034831.974 * 10%1.0680.5841

Wnless otherwise specified, the precision of the data is +3°A.

TABLE XI

RATIO OF OBSERVED-TO-CALCULATED “Y(n,2n)wY ACTIVATIONS

Distance From Source

Calculation 22.2mm 50.0mm 76.15mm 126.0mm 200.0mm 300.0mm

I 0.752 0.740 0.726 0.740 0.803 0.934II 0.936 0.926 0.883 0.847 0.848 0.924III 1.008 1.067 0.993 0.964 0.938 1.048Iv 1.026 1.059 1.041 0.983 0.964 1.079

.

spectrum at this point consists mainly of the unat-tenuated 14-MeV component. There is also a low-energy component from backscattered neutrons, butthis contributed negligibly to the (n,2n) activations.Moreover, the (n,2n) activation cross sections aregenerally kncpvnto within a few per cent in the re-quired energy range. Hence, we disregard the dis-crepancies at 22.2 mm. At the other radii, Calcula-

tion IV seems to be in generally good agreement withthe experiment. Moat of the remaining discrepanciescan plausibly be attributed to errors in the activa-tion cross sections. However, the results do suggestthat there may be some small errorsin the total crosssections for ‘Li or deuterium in the 14-MeV region.This is surmised because the observed-to-calculatedratio for a given activation generally decreases with

25

TABLE XII

RATIO OF OBSERVED-TO-CALCULATEDRADIOCHEMICAL ACTIVATIONS (CALCULATION IV)

Distance From Source

Reaction 22.2mm 50.0mm 76.15mm

‘W(n,2n)”Y‘Zr(n,2n)”Zr‘eWm(n, 2n)’%“iIr(n,2n) ‘WIr‘oTAu(n,2n)lnAu‘a1U(n,2n)a17UW.r(n,2n) lo%

+ W.r(n,~)iwsIrlw~(n,n, )Iwmfi

‘“’U(n,f)”Mo‘WJ(n,f)WMo“Sc(n,y)’”SclsY(n,~)mYW(’m(n,7)i7”Tm‘s7Au(n,~)lWAu2uU(n,7)210U

1,256 1.0350.9831.0040.999

1.135 0.9791.136 1.102

1.061

0.7441.030

1.163 0.9921.054

0.971 1.0150.962

1.026 1.0591,438 1.243

1.1

m

1

II

I

I

f090.8

to.,o~RADIUS (mm)

Fig. 4.

1.0390.9920.9970.9840.9741.0571.062

0.7931.0010.9991.0771.0280.9431.0411.189

E

a9$

[

126.0 mm 200.0 mm 300.0mm

0.9840.9411.0030.9210.9391.0320.994

0.9081.0040.9981.0841.0110.8780.9831.129

1.0200.8490.9920.9160.9251.0581.007

1.4630.9890.9951.0850.9780.8600.9641.107

0.9660,8190.9730.8750.9191.0851.046

1.0471.1211.4380.9911.4041.0791.166

‘“’r——’———1.2~

I ‘zr( ~2n)%r ACTIVATION

1.1

1.0

091 I0.8

t

—

0.7: I I 1 I I I50 1001s02002s0300

RADIUS (mm)

Fig. 5.Ratio of observed-to-calculated 8’Y(n,2n)8’Y Ratio of observed-to-~alculated ‘0Zr(n,2n)”Zr

.,

. .

.

.

activation us radius. The error bars are from activation us radius. The error bars are fromexperimental uncertainties only. The experimental uncertainties only. Thethreshold energy is 11.60 MeV. threshold energy is 12.12 Me V.

26

‘“’v—————l%m(n,2n)%m M.711VAl10N

1.2t

I

o.,~o 50 100 150 m 2s0 300

RADIUS (mm)

Fig. 6.Ratio of observed-to-calculated1eeTm(n,2n)1e8Tm activation us radius. Theerror bars are from experimental uncertaintiesonly. The threshold energy h 8.11 MeV.

‘l-————1

1-0.8,

‘Ir(n,2nfir ACTIVATION

0.7LLLUJJJo 50 NM 150 m 250 300

RADIUS (mm)

Fig. 7.Ratio of observed-to-calculated “11r(n,2n)1WIractivation us radius. The error bars are fromexperimental uncertainties only. Thethreshold energy is 8.17 Me V.

1.3-I I I I I i

f

12 - l~&(n,2n) ‘% IMTIVATION

1.1– [

1.0–

‘h f]_09 -

0.8 -

o.,o~RADIUS (mm)

Fig. 8.

Ratio of observed-to-calculated1WAu(n,2n)’WAu activation us radius. The errorbars are from experimental uncertainties only.The threshold energy is 8.12 MeV.

1.3- I I 1 I I I

12 - %J(n,2n)% KTIVATION

0.8

to.,~o 50 100 150 200 2!50 m

RADIUS (mm)

Fig. 9.Ratio of observed-to-calculated 2MU(n,2n)M7Uactivation us mdius. The error bars are fromexperimental uncertainties only. Thethreshold energy is 6.17 Mel?

27

1.3 I I I I I I

l~lr(%~) ‘=Ir +lwIr(n,y) ‘qr ACTIVATION1.2–

1.1–

H

1.0–I [ I

09 –

0.8

t 1RADIUS (mm)

Fig. 10.Ratio of observed-to-calculated “’Ir(n,2n)’’21r+ 1911r(n,y)loXIractivation us radius. The errorbars are from experimental uncertainties only.

increasing radial source distance. This behavior isparticularly pronounced for the highest thresholdtarget, ‘OZr(threshold energy 12.12MeV), and is es-sentially absent from the “U(n,2n) results, whichhave a significantly larger contribution from down-scattered neutrons at the larger radii. Optimumagreement between the (n,2n) data and calculationsis obtained by an upward resealing of all ‘Li ordeuterium cross sections by 4 and 3%, respectively,in the 14-MeV region. The production of ‘921ris dueto both (n,2n) and (n, ~) reactions. TheleoIr(n,2n)lBiIrreaction contributes more than 70% tothe total, except at 200 mm where the contributionis -56°\0.

B. The (n,f) Activations

The (n)f) activations of ‘“U and ’80U wereobserved. The mu(n,fl reaction has an effective

threshold of -1 MeV with most of the activationresulting from neutrons above 5 MeV. The reactioncross section is thus similar to that of the ‘80U(n,2n)and 7Li(n,n’a) reactions. The results of CalculationIV are given in Table XII and shown in Figs. 11 and12. Disregarding the 22.2-mm data, Calculation IV

1.3I I I I I I

2%J (n,f )% ACTIVATION1.2–

:.: -1[[~~-

09 –

LJLuI0 so 100 1s0 200 2s0 300

RADIU8 (mm)

Fig. 11.Ratio of observed-to-calculated ‘sU(n,f)WMoactivation us radius. The error bars are fromexperimental uncertainties only.

‘%(n ,f ) % ACTIVATNX4

\![l

RADIUS (mm)

F%. 12.Ratio of observed-to-calculated ‘J’U(n,f)”Moactivation us radius. The error bars are fromexperimental uncertainties only.

.

..

.

.

28

is in satisfactory agreement with experiment, exceptpossibly at the 300-mm radius at the outside of theLiD sphere. The reason for this discrepancy is notclear, because the fission cross section is thought tobe known to within a few per cent.

The 28VJ(n,f) activation is due to the entireneutron energy spectrum present in this experiment.It is the first radiochemical activation discussed sofar that probes the lower energy region of thespectrum. Calculation IV and the experiment are insatisfactory agreement everywhere.

The two Monte Carlo calculations give (n,f) ac-tivations that agree everywhere within 1%. The twoS. calculations are not in such close agreement witheach other or with the Monte Carlo results. Calcula-tion II, the most reliable S“ computation, is insomewhat better agreement with the experimentthan Calculation I is. The ‘a6U(n,fl results for thevarious calculations are given in Table X111. The2a’U(n,f) results are similar.

C. The (n,y) Activations

The (n,y) activations of five different target nucleiwere measured in this experiment. The (n,~) crosssections for these targets generally rise rapidly withdecreasing energy, so that these activations comeprimarily from the lower energy range of the neutronspectra. Typically 70% of the activations come fromneutron energies less than 70 keV, except at the 22.2-mm radius where there is a significant 14-MeV con-tribution. These activations provide a stringent testof the transport codes, because the lower energyregion of the neutron spectrum is populated through

TABLE

successive downscattering interactions. Unfor-tunately, the (n,~) reaction cross sections for most ofthe target nuclei used are not well known.

The results of Calculation IV are given in TableXII and shown in Figs. 13-17. Only for gold, whoseactivation cross section is thought to be well known,are Calculation IV and the experiment in satisfac-tory agreement everywhere. Satisfactory agreementfor scandium, yttrium, and thulium is also obtainedeverywhere except possibly at the 300-mm position,

I I I I I1.5 -

%c(n,y)%c JWTIVATION ,,

1.4“

p 1.3-

8

31.2 -

2g ,J .

!!l

~] I 1

1.0–

Q9t i

.o~m 100 m m 250 300

RADIUS (mm)

Fig. 13.Ratio of observed-to-calculated 4’Sc(n,y)46Scactivation us radius. The error bars are fromexperimental uncertainties only.

XIII

RATIO OF OBSERVED-TO-CALCULATED ‘88U(n,f)”Mo ACTIVATIONS

Distance From Source

Calculation 50.0mm 76.15mm 126.0mm 200.0mm 300.0mm

I 0.880 0.844 0.879 0.925 1.099II 0.964 0.908 0.904 0.888 0.988m 1.036 0.990 1.000 0.978 1.039lv 1.030 l.ml 1.004 0.989 1.047

29

13 I I I I I I I1.2– *(n,y)% JWTIVATION -

1.1–

1.0– ~~11 ~ p

09 –

0.8 –

0.70 I I I 1 I I50 100 130 200 2343 300

RADIUS (mm)

Fig. 14.Ratio of observed-to-calculated “Y(n,~)wYac-tivation vs radius. The error bars are from ex-perimental uncertainties only.

I I I I I1.s–

1.4

t

‘Tm(n,y) I%m ACTIVATION -

0.9

t

1-

~o-RADIUS (mm)

Fig. 15.Ratio of observed-to-calculatedl@@Tm(n, y) 170Tm activation vs radius. The

error bars are from experimental uncertaintiesonly.

I

LJ_-0 30 [001 s020023030

RADIUS (mm)

Fig. 16.Ratio of observed-to-calculated“7Au(n,y)’”Au activation vs radius. The errorbars are from experimental uncertainties only.

p~(n,y)~ KTIVATION

1.4

Q9

t

RADiUS (mm)

Fig. 17.Ratio of observed-to-calculated “’U(n,7)’”Uactivation vs radius The error bars are fromexperimental uncertainties only.

.L

.,

.

●

30

>’

. .

‘A

“.

where there are rather large discrepancies in thescandium and thulium results. The calculated2’8U(n,~) activations are everywhere smaller thanobserved (generally by 10 to 207.), suggesting thatthe activation cross section used is too small, par-ticularly in the 14-MeV region, because the dis-crepancy is even larger at 22.2 mm. Note that thepostulated off-center position of the experimentalsource is not expected to influence the (n,~) activa-tions at 22.2 mm by more than a few per cent. Final-ly, the fact that the observed-to-calculated activa-tion ratio is generally large at 300 mm, the outaideposition, suggests that there may be some roomreturn, which has been neglected in the calculations.

A calculation that attempted to simulate the roomreturn, however, failed to significantly modify theresults. Moreover, if sufficient room return were pre-sent to explain the scandium and thulium dis-crepancies, a large discrepancy would then be in-troduced in the gold results at 300 mm because ofthe large value of the Au(n,~) cross section at verylow energies.

As for the (n,f) activations, the two Monte Carlocalculations are in very close agreement. This is notsurprising because Calculation III is used to providethe lower energy fluences for Calculation IV. Thetwo S. calculations are in much poorer agreementwith the experiment; the more reliable 21-groupcalculation gives somewhat better results. Theresultsof the four calculations of the Au(n,~) activa-tions, which are typical, are”given in Table XIV.

D. The “’Ir(n,n’)’’’mIr Activation

The cross section for the Issfi(n,n’)igsmbreaction isvery poorly known. Consequently, we considerCalculation IV to be in satisfactory agreement withthe experiment (see Table XII).

V. CONCLUSIONS

It seems, on the basis of this experiment, that ourunderstanding of neutron transport through OLiDisessentially correct. In most cases, discrepancies be-tween calculation and experiment can be plausiblyexplained in terms of imprecisely known cross sec-tions. The cross-section data relevant to transportthrough ‘LiD appear to be essentially correct,although there is some indication that the 14-MeVinelastic or nonforward elastic cross sections ondeuterium and/or *Li may be a few per cent toosmall. The cross-section data used for the (n,2n) and(n,f) activations seem to be basically correct. Ex-cept for mu(n,~), the (n,y) activation cross sections

also seem to be reasonably accurate, even thoughonly the cross sections for gold are well known ex-perimentally. The ‘Li(n,n’a) cross-section data arequite possibly in error (too high) by -15% in the 14-MeV region, whereas the ‘Li(n,a) cross sectionsseem to be quite accurate.

For neutron-transport computations, the MonteCarlo methods provide more realistic results than do

TABLE XIV

RATIO OF OBSERVED-TO-CALCULATED ‘WAu(n,y)’”Au ACTIVATIONS

Distance From Source

Calculation 22.2mm 50.0mm 76.15mm 126.0mm 200.Omm 300.0nun— —

I 0.752 0.740 0.726 0.740 0.803 0.934II 0.936 0.926 0.883 0.847 0.848 0.924III 1.008 1.067 0.993 0.964 0.938 1.048Iv 1.026 1.059 1.041 0,983 0.964 1.079

31

the S. techniques, although they require signifi-cantly more machine time. It is reassuringthat ourmost realistic simulation of the experiment,Calculation IV, provides the best overall fit to thedata. We believe that further improvement in thecalculation could be obtained only with the incor-poration of improved nuclear data.

ACKNOWLEDGMENTS

I would like to thank the following people foruseful discussions and encouragement: D. W. Barr,D. W. Muir, W. E. Preeg, J. C. Solem, and P. P.Whalen. Particular thanks are due to J. S. Hen-dricks, who compiled the radiochemical-activationcross-section data and evaluated the radiochemical-activation integrals. Those who participated in theradiochemical-activation experiment were D. W.Barr, G. W. Knobelock, B. P. Bayhurst, R. J.Prestwood, J. S. Gilmore, K. Wolfsberg, G. P. Ford,V. M. Armijo, T. D. Baker, J. E. Hasty, and J.Drake.

REFERENCES

1.

2.

J. S. Hendricks, Los Alamos ScientificLaboratory internal document (May 14, 1976).

L. L. Carter, E. D. Cashwell, C. J. Everett, C. A.Forest, R. G. Schrandt, W. M. Taylor, W. L.

3.

4.

5.

6.

7,

Thompson, and G. D. Turner, “Monte CarloCode Development in Los Alamos,” Los AlamosScientific Laboratory report LA-5903-MS(March 1975).

E. D. Cashwell, J. R. Neergaard, W. M. Taylor,and G. D. Turner, “MCN: A Neutron MonteCarlo Code, ” Los Alamos Scientific Laboratoryreport LA-4751 (January 1972).

D. W. Muir and M. E. Wyman, “A Tritium-Production Measurement with Application toFusion Reactor Blanket Design,” ‘Ilans. Am.Nucl. Sot. 15, 631 (1972).

W. A. Reupke and D. W. Muir, “Neutronic DataConsistency Analysis for Lithium Blanket andShield Design,” 2nd Top. Meet. Technol. Con-trol. Nucl. Fusion, Rlchland, Washington, Sep-tember 21-23, 1976 (Electric Power Research In-stitute, Palo Alto, CA 94304).

W. A. Reupke, “The Consistency of Differentialand Integral Thermonuclear Neutronics Data, ”(Ph.D. thesis, Georgia Institute of Technology,Atlanta, GA 30332, 1977), Los Alamos ScientificLaboratory report LA-7067-T (January 1978).

D. W. Barr, Los Alamos Scientific Laboratory in-ternal document (May 27, 1976).

‘t

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32

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